Power
Adds 25% damage to all RAW (physical) damage you do in Sword mode.
Element
Adds 25% damage to all Elemental damage you do in Sword mode.
Dragon
Adds Dragon element to all your attacks in Sword mode, which is the type of damage Dragons are the weakest to (i.e. Rathian, Rathalos). The exact amount depends on the weapon.
Paralysis
Attacks in sword mode will do paralysis. The exact amount depends on the weapon.
After doing enough Paralysis damage to a monster they'll be stunned for a short while. The amount of paralysis damage you need to inflict, and the duration of the monsters stun, varies based on the monster. Take note that after you stun a monster, it becomes harder to stun it again. Additionally, paralysis damage is "removed" from a monster over time, so you need to keep attacking in order to paralyze the monster.
Poison
Attacks in sword mode will do poison damage. The exact amount depends on the weapon.
After you inflict enough poison damage on a monster they will be poisoned for a predetermined duration, and will take damage over time. Like paralysis, the duration and amount of poison damage required to inflict it depends on the monster. It will also be removed over time, and becomes harder to apply on the monster with each successful application of it.
Exhaust
Attacks in Sword Mode will do Exhaust damage. The exact amount depends on the weapon.
Exhaust damage inflicted on the monsters head will do KO damage. After a certain amount of KO damage is dealt the monster will be knocked over for a short period. Do note that like other status ailments the KO damage inflicted on the monster will decrease over time, so it's important to keep attacking the head if you wish to knock the monster out.
Exhaust Damage inflicted anywhere but the head will do stamina damage, which drains the monsters stamina. When using a Switch Axe that does exhaust damage you'll notice monsters will begin drooling a lot faster than normal, resulting in them being less effective in battle.
All weapon attacks are performed by using the A and X buttons with directional keys. The combo you're talking about is most likely what is called the "Alternating Slashes" combo. This is performed after an Upswing (Down + A) by hitting Up or Down.
Note that you cannot chain a side-step after this attack, leaving you somewhat vulnerable. If you have enough to time to perform multiple Alternating Slashes, it is probably more damage-efficient to use the charging thrust of the Sword Form.
A good guide for Switch Axe combos can be found here.
Best Answer
Size has no effect on what materials are gathered from the monster, but it does have an effect on monster stats. Larger monsters deal slightly more damage and a little bit more health and the opposite is true for small monsters. Certain event quests, however, are the exception to this rule. For example, there is an Uragaan hunting quest where the Uragaan in question is about the size of a Jaggi, yet has the exact same stats of an Uragaan of normal size.